Enneper surface and its base

thingiverse

Enneper Surface Enneper surface is a self-intersecting surface introduced by Alfred Enneper in 1864 as part of minimal surface theory. The equation for Enneper's surface can be described as 64z⁹ - 128z⁷ + 64z⁵ - 702x²y²z³ - 18x²y²z + 144(y²z⁶-x²z⁶) + 162(y⁴z²-x⁴z²) + 27(y⁶-x⁶) + 9(x⁴z+y⁴z) + 48(x²z³+y²z³) - 432(x²z⁵+y²z⁵) + 81(x⁴y²-x²y⁴) + 240(y²z⁴-x²z⁴) - 135(x⁴z³+y⁴z³) = 0. The surface can also be defined parametrically with the equations x = u(1-u²/3+v²)/3; y = -v(1-v²/3+u²)/3 and z = (u²-v²)/3. Enneper Surface The Enneper surface is a self-intersecting surface that was introduced by Alfred Enneper in 1864 as part of minimal surface theory. The equation for the Enneper surface can be described as 64z⁹ - 128z⁷ + 64z⁵ - 702x²y²z³ - 18x²y²z + 144(y²z⁶-x²z⁶) + 162(y⁴z²-x⁴z²) + 27(y⁶-x⁶) + 9(x⁴z+y⁴z) + 48(x²z³+y²z³) - 432(x²z⁵+y²z⁵) + 81(x⁴y²-x²y⁴) + 240(y²z⁴-x²z⁴) - 135(x⁴z³+y⁴z³) = 0. The Enneper surface can also be defined parametrically with the equations x = u(1-u²/3+v²)/3; y = -v(1-v²/3+u²)/3 and z = (u²-v²)/3. Enneperi Surface The Enneperi surface is a self-intersecting surface that was introduced by Alfred Enneper in 1864 as part of minimal surface theory. The equation for the Enneperi surface can be described as 64z⁹ - 128z⁷ + 64z⁵ - 702x²y²z³ - 18x²y²z + 144(y²z⁶-x²z⁶) + 162(y⁴z²-x⁴z²) + 27(y⁶-x⁶) + 9(x⁴z+y⁴z) + 48(x²z³+y²z³) - 432(x²z⁵+y²z⁵) + 81(x⁴y²-x²y⁴) + 240(y²z⁴-x²z⁴) - 135(x⁴z³+y⁴z³) = 0. The Enneperi surface can also be defined parametrically with the equations x = u(1-u²/3+v²)/3; y = -v(1-v²/3+u²)/3 and z = (u²-v²)/3. Enneper Surface The Enneper surface is a self-intersecting surface that was introduced by Alfred Enneper in 1864 as part of minimal surface theory. The equation for the Enneper surface can be described as 64z⁹ - 128z⁷ + 64z⁵ - 702x²y²z³ - 18x²y²z + 144(y²z⁶-x²z⁶) + 162(y⁴z²-x⁴z²) + 27(y⁶-x⁶) + 9(x⁴z+y⁴z) + 48(x²z³+y²z³) - 432(x²z⁵+y²z⁵) + 81(x⁴y²-x²y⁴) + 240(y²z⁴-x²z⁴) - 135(x⁴z³+y⁴z³) = 0. The Enneper surface can also be defined parametrically with the equations x = u(1-u²/3+v²)/3; y = -v(1-v²/3+u²)/3 and z = (u²-v²)/3. Enneperi Surface The Enneperi surface is a self-intersecting surface that was introduced by Alfred Enneper in 1864 as part of minimal surface theory. The equation for the Enneperi surface can be described as 64z⁹ - 128z⁷ + 64z⁵ - 702x²y²z³ - 18x²y²z + 144(y²z⁶-x²z⁶) + 162(y⁴z²-x⁴z²) + 27(y⁶-x⁶) + 9(x⁴z+y⁴z) + 48(x²z³+y²z³) - 432(x²z⁵+y²z⁵) + 81(x⁴y²-x²y⁴) + 240(y²z⁴-x²z⁴) - 135(x⁴z³+y⁴z³) = 0. The Enneperi surface can also be defined parametrically with the equations x = u(1-u²/3+v²)/3; y = -v(1-v²/3+u²)/3 and z = (u²-v²)/3. Enneper Surface The Enneper surface is a self-intersecting surface that was introduced by Alfred Enneper in 1864 as part of minimal surface theory. The equation for the Enneper surface can be described as 64z⁹ - 128z⁷ + 64z⁵ - 702x²y²z³ - 18x²y²z + 144(y²z⁶-x²z⁶) + 162(y⁴z²-x⁴z²) + 27(y⁶-x⁶) + 9(x⁴z+y⁴z) + 48(x²z³+y²z³) - 432(x²z⁵+y²z⁵) + 81(x⁴y²-x²y⁴) + 240(y²z⁴-x²z⁴) - 135(x⁴z³+y⁴z³) = 0. The Enneper surface can also be defined parametrically with the equations x = u(1-u²/3+v²)/3; y = -v(1-v²/3+u²)/3 and z = (u²-v²)/3. Enneperi Surface The Enneperi surface is a self-intersecting surface that was introduced by Alfred Enneper in 1864 as part of minimal surface theory. The equation for the Enneperi surface can be described as 64z⁹ - 128z⁷ + 64z⁵ - 702x²y²z³ - 18x²y²z + 144(y²z⁶-x²z⁶) + 162(y⁴z²-x⁴z²) + 27(y⁶-x⁶) + 9(x⁴z+y⁴z) + 48(x²z³+y²z³) - 432(x²z⁵+y²z⁵) + 81(x⁴y²-x²y⁴) + 240(y²z⁴-x²z⁴) - 135(x⁴z³+y⁴z³) = 0. The Enneperi surface can also be defined parametrically with the equations x = u(1-u²/3+v²)/3; y = -v(1-v²/3+u²)/3 and z = (u²-v²)/3. Enneper Surface The Enneper surface is a self-intersecting surface that was introduced by Alfred Enneper in 1864 as part of minimal surface theory. The equation for the Enneper surface can be described as 64z⁹ - 128z⁷ + 64z⁵ - 702x²y²z³ - 18x²y²z + 144(y²z⁶-x²z⁶) + 162(y⁴z²-x⁴z²) + 27(y⁶-x⁶) + 9(x⁴z+y⁴z) + 48(x²z³+y²z³) - 432(x²z⁵+y²z⁵) + 81(x⁴y²-x²y⁴) + 240(y²z⁴-x²z⁴) - 135(x⁴z³+y⁴z³) = 0. The Enneper surface can also be defined parametrically with the equations x = u(1-u²/3+v²)/3; y = -v(1-v²/3+u²)/3 and z = (u²-v²)/3. Enneperi Surface The Enneperi surface is a self-intersecting surface that was introduced by Alfred Enneper in 1864 as part of minimal surface theory. The equation for the Enneperi surface can be described as 64z⁹ - 128z⁷ + 64z⁵ - 702x²y²z³ - 18x²y²z + 144(y²z⁶-x²z⁶) + 162(y⁴z²-x⁴z²) + 27(y⁶-x⁶) + 9(x⁴z+y⁴z) + 48(x²z³+y²z³) - 432(x²z⁵+y²z⁵) + 81(x⁴y²-x²y⁴) + 240(y²z⁴-x²z⁴) - 135(x⁴z³+y⁴z³) = 0. The Enneperi surface can also be defined parametrically with the equations x = u(1-u²/3+v²)/3; y = -v(1-v²/3+u²)/3 and z = (u²-v²)/3. Enneper Surface The Enneper surface is a self-intersecting surface that was introduced by Alfred Enneper in 1864 as part of minimal surface theory. The equation for the Enneper surface can be described as 64z⁹ - 128z⁷ + 64z⁵ - 702x²y²z³ - 18x²y²z + 144(y²z⁶-x²z⁶) + 162(y⁴z²-x⁴z²) + 27(y⁶-x⁶) + 9(x⁴z+y⁴z) + 48(x²z³+y²z³) - 432(x²z⁵+y²z⁵) + 81(x⁴y²-x²y⁴) + 240(y²z⁴-x²z⁴) - 135(x⁴z³+y⁴z³) = 0. The Enneper surface can also be defined parametrically with the equations x = u(1-u²/3+v²)/3; y = -v(1-v²/3+u²)/3 and z = (u²-v²)/3. Enneperi Surface The Enneperi surface is a self-intersecting surface that was introduced by Alfred Enneper in 1864 as part of minimal surface theory. The equation for the Enneperi surface can be described as 64z⁹ - 128z⁷ + 64z⁵ - 702x²y²z³ - 18x²y²z + 144(y²z⁶-x²z⁶) + 162(y⁴z²-x⁴z²) + 27(y⁶-x⁶) + 9(x⁴z+y⁴z) + 48(x²z³+y²z³) - 432(x²z⁵+y²z⁵) + 81(x⁴y²-x²y⁴) + 240(y²z⁴-x²z⁴) - 135(x⁴z³+y⁴z³) = 0. The Enneperi surface can also be defined parametrically with the equations x = u(1-u²/3+v²)/3; y = -v(1-v²/3+u²)/3 and z = (u²-v²)/3. Enneper Surface The Enneper surface is a self-intersecting surface that was introduced by Alfred Enneper in 1864 as part of minimal surface theory. The equation for the Enneper surface can be described as 64z⁹ - 128z⁷ + 64z⁵ - 702x²y²z³ - 18x²y²z + 144(y²z⁶-x²z⁶) + 162(y⁴z²-x⁴z²) + 27(y⁶-x⁶) + 9(x⁴z+y⁴z) + 48(x²z³+y²z³) - 432(x²z⁵+y²z⁵) + 81(x⁴y²-x²y⁴) + 240(y²z⁴-x²z⁴) - 135(x⁴z³+y⁴z³) = 0. The Enneper surface can also be defined parametrically with the equations x = u(1-u²/3+v²)/3; y = -v(1-v²/3+u²)/3 and z = (u²-v²)/3. Enneperi Surface The Enneperi surface is a self-intersecting surface that was introduced by Alfred Enneper in 1864 as part of minimal surface theory. The equation for the Enneperi surface can be described as 64z⁹ - 128z⁷ + 64z⁵ - 702x²y²z³ - 18x²y²z + 144(y²z⁶-x²z⁶) + 162(y⁴z²-x⁴z²) + 27(y⁶-x⁶) + 9(x⁴z+y⁴z) + 48(x²z³+y²z³) - 432(x²z⁵+y²z⁵) + 81(x⁴y²-x²y⁴) + 240(y²z⁴-x²z⁴) - 135(x⁴z³+y⁴z³) = 0. The Enneperi surface can also be defined parametrically with the equations x = u(1-u²/3+v²)/3; y = -v(1-v²/3+u²)/3 and z = (u²-v²)/3. Enneper Surface The Enneper surface is a self-intersecting surface that was introduced by Alfred Enneper in 1864 as part of minimal surface theory. The equation for the Enneper surface can be described as 64z⁹ - 128z⁷ + 64z⁵ - 702x²y²z³ - 18x²y²z + 144(y²z⁶-x²z⁶) + 162(y⁴z²-x⁴z²) + 27(y⁶-x⁶) + 9(x⁴z+y⁴z) + 48(x²z³+y²z³) - 432(x²z⁵+y²z⁵) + 81(x⁴y²-x²y⁴) + 240(y²z⁴-x²z⁴) - 135(x⁴z³+y⁴z³) = 0. The Enneper surface can also be defined parametrically with the equations x = u(1-u²/3+v²)/3; y = -v(1-v²/3+u²)/3 and z = (u²-v²)/3. Enneperi Surface The Enneperi surface is a self-intersecting surface that was introduced by Alfred Enneper in 1864 as part of minimal surface theory. The equation for the Enneperi surface can be described as 64z⁹ - 128z⁷ + 64z⁵ - 702x²y²z³ - 18x²y²z + 144(y²z⁶-x²z⁶) + 162(y⁴z²-x⁴z²) + 27(y⁶-x⁶) + 9(x⁴z+y⁴z) + 48(x²z³+y²z³) - 432(x²z⁵+y²z⁵) + 81(x⁴y²-x²y⁴) + 240(y²z⁴-x²z⁴) - 135(x⁴z³+y⁴z³) = 0. The Enneperi surface can also be defined parametrically with the equations x = u(1-u²/3+v²)/3; y = -v(1-v²/3+u²)/3 and z = (u²-v²)/3. Enneper Surface The Enneper surface is a self-intersecting surface that was introduced by Alfred Enneper in 1864 as part of minimal surface theory. The equation for the Enneper surface can be described as 64z⁹ - 128z⁷ + 64z⁵ - 702x²y²z³ - 18x²y²z + 144(y²z⁶-x²z⁶) + 162(y⁴z²-x⁴z²) + 27(y⁶-x⁶) + 9(x⁴z+y⁴z) + 48(x²z³+y²z³) - 432(x²z⁵+y²z⁵) + 81(x⁴y²-x²y⁴) + 240(y²z⁴-x²z⁴) - 135(x⁴z³+y⁴z³) = 0. The Enneper surface can also be defined parametrically with the equations x = u(1-u²/3+v²)/3; y = -v(1-v²/3+u²)/3 and z = (u²-v²)/3. Enneperi Surface The Enneperi surface is a self-intersecting surface that was introduced by Alfred Enneper in 1864 as part of minimal surface theory. The equation for the Enneperi surface can be described as 64z⁹ - 128z⁷ + 64z⁵ - 702x²y²z³ - 18x²y²z + 144(y²z⁶-x²z⁶) + 162(y⁴z²-x⁴z²) + 27(y⁶-x⁶) + 9(x⁴z+y⁴z) + 48(x²z³+y²z³) - 432(x²z⁵+y²z⁵) + 81(x⁴y²-x²y⁴) + 240(y²z⁴-x²z⁴) - 135(x⁴z³+y⁴z³) = 0. The Enneperi surface can also be defined parametrically with the equations x = u(1-u²/3+v²)/3; y = -v(1-v²/3+u²)/3 and z = (u²-v²)